which take the same forms as their classical ones, but all the quantities now represent their expectation values, \(A_I \equiv \left<\widehat{{A}_I}\right>\) .
Then, it was found that the effective Hamiltonian is given by [1]},
\({{\cal {H}}}_{\text{eff.}} = - \frac{3}{8\pi \gamma ^2 \bar{\mu }^2 G}|p|^{1/2}\sin ^2(\bar{\mu }c) + \frac{1}{2}|p|^{3/2} p_{\phi }^2,\) 
